Term for a graph with a regular polygon with labeled points and an irregular polygon inside of it

Solution 1:

In data visualization, it is called a

radar or spider chart

because it looks like either a radar screen with the values as you go around the circle, or it just sort looks like a spider's web.

It is essentially a bar chart or line chart of a small set on the same scale that, instead of being arranged linearly, is arranged circularly. The spider's web is like the y-axis on a linear chart, and the colored part is the value of each item.

Placing radar charts side by side allows a comparison of many dimensions at once based on comparison of the shapes (a much more accessible comparison than Chernoff faces. It is similar to Nightingale's famous rose chart but the latter implies a cyclical order to the categories whereas a radar chart involves unordered categories.

FiveThirtyEight has a good use of radar charts to compare candidates. (see the graphic just above 'Group 1').

Solution 2:

Polygon-circle graph

This kind of graph is called a ‘polygon-circle graph’, according to this Wikipedia article.